Free-associate with the word Venice, and likely responses will include gondoliers, canals, romance. A cynic might have different rejoinders: flooding, crowds, subpar restaurants. But most visitors to this island city would agree that it is a destination unlike any other—a sensory overload, especially for the eyes. Streets throb with throngs seduced by the panoply of shop windows and their riotous displays of masks, handmade papers, and glass. Museums and cathedrals house older artworks, and around each corner is another uniquely Venetian view of an arched bridge or a hidden piazza. The city has only 60,000 residents, but millions of tourists descend annually, and each summer weekend brings a crush of pedestrians. Thus, while in-town accommodation has the advantage of being close to the action, at the end of the day it can be a relief to detach from the phantasm and retreat to another island just a 10-minute boat ride away, one whose sole occupant is the San Clemente Palace.

The quiet is a palpable jolt when you disembark. Through some sonic illusion, even the motorboat activity on the Venetian lagoon is silenced, and the only sounds are your own footfalls on the long stone walkway that leads from the dock to the front door of the former monastery, whose residents were mapmakers. The immense 17th-century edifice, which was restored and opened as a hotel in 2003, enfolds several courtyards and is a terra-cotta-colored stucco showplace. It is not an imaginative stretch to envision friars making their way to vespers through the hushed corridors, even as you pad through the maze of hallways in a terry robe and slippers, trying not to become lost on the way to the spa. Adding to the reverential atmosphere is the adjoining Church of San Clemente, which dates to 1150.

The 200-room hotel occupies four acres, but the rest of the 17-acre island is hotel property as well, with a three-hole golf course, a pool, tennis courts, and gardens that beckon you to sit a spell. Although Venice is not known for its fine dining, Ca dei Frati, the hotel’s paean to haute cuisine, is a place for dinner with no risk of disappointment. A seafood course of rock lobster with prosciutto and cauliflower mousse proves a good choice but a difficult one, when other options are prawns with zuppa fagioli, and sea bass with black truffles.

The isolated nature of an island defines both its virtues and drawbacks. But with a private launch departing San Clemente for Piazza San Marco every 20 minutes, you can float back into the cinema verité that is Venice whenever you choose. Staying in a converted monastery allows time for meditation, which is not an unwelcome undertaking. In a silent, centuries-old courtyard just minutes from the Doges’ Palace, you cannot help but reflect that despite all the city’s structural problems—the sinking Piazza San Marco, basilicas with flooded floors, and buildings that almost crumble before your eyes in the damp salt air—Venice will somehow endure, with characteristic gusto, for another millennium.